In drug-drug interaction (DDI) research, to fully understand multiple drugs'pharmacokinetics and their interactions, a physiologically based pharmacokinetic model (PBPK) is the only viable means of investigating and quantifying all the interacting factors (active sites or organs). A PBPK model is known for its model identification problem because of its complex structure;hence, it usually borrows prior physiological information to make the model identifiable. However, conventional DDI researches based on deterministic PBPK models ignore population variations in PK parameters, experimental noise and uncertainties in prior knowledge, which in turn leads to subjective conclusions with unknown reliability. This grant application proposes a system of Bayesian tools to meet these pharmacological, statistical and computational challenges of PBPK models by exploring three aims. In Aim 1, individual drug's PBPK models of the inhibitor-substrate combination is established based on their published animal, in-vitro, and in-vivo data;the strategy of starting a simple model with limited information to a complex model with rich knowledge is systematically discussed;and Bayesian meta-analysis methods are proposed. In Aim 2, based on clinical DDI studies, a two-stage Bayesian method for a joint inhibitor-substrate PBPK model is developed;a predictive false negative rate is proposed to evaluate the DDI prediction;and Bayesian model selection procedures are implemented to select the best PBPK model among competitive ones. In Aim 3, all the prescribed Bayesian tools are implemented in R, a statistical and computational freeware;and its web-based application is developed to facilitate its usage for general research scientists. In this grant application, we realize the fact that the DDI is enzyme-dependent. Hence, a CYP3A specific inhibitor-substrate combination, ketoconazole-midazolam, is chosen as a starting example. It will serve as a building block for multi-enzyme and multi-drug based DDI PBPK models.